<html>
   <head>
      <title>Solvable Info</title>

      <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">

      <link rel="icon" type="image/png" href="./images/favicon.png"></link>
      <link rel="stylesheet" href="./style/fonts.css" type="text/css">

      <script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.js"></script>
      <script type="text/x-mathjax-config">
       MathJax.Hub.Config({
      	  CommonHTML: {
             scale: 90,
          },
       });
      </script>
      <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=MML_CHTML"></script>
      <script src="./build/allGroupExplorer.js"></script>
      <script src="./build/allSheets.js"></script>
      <script src="./SolvableInfo.js"></script>
   </head>

   <body>
      <template id="header">
         <h3>${MathML.sans('<mtext>Results of &#8220;Solvable group&#8221; computation for&nbsp;</mtext>' + group.name)}</h3>
      </template>
      <template id="abelian">
         ${MathML.sans(group.name)} is <a href="./help/rf-groupterms/index.html#solvable-group-solvable-decomposition">solvable</a>
         because it is <a href="./help/rf-groupterms/index.html#abelian-group">abelian</a>.
      </template>
      <template id="solvable">
         ${MathML.sans(group.name)} is a <a href="./help/rf-groupterms/index.html#solvable-group-solvable-decomposition">solvable</a>
         group by the following solvable decomposition:
         <ul id="decomposition" style="list-style-type: none">
         </ul>

         <p>In summary, ${decompositionDisplay}.</p>

         <p>You can see a diagram of all the groups in the solvable decomposition,
            including quotient maps, by
            <a href="javascript:showSolvableDecompositionSheet('CDElement')">Cayley diagram</a>,
            <a href="javascript:showSolvableDecompositionSheet('CGElement')">cycle graph</a>, or
            <a href="javascript:showSolvableDecompositionSheet('MTElement')">multiplication table</a>.
         </p>
      </template>
      <template id="decomposition_element">
         <li>The <a href="./help/rf-groupterms/index.html#quotient-group">quotient</a> of
            ${makeGroupRef(g)}</a> by its
            <a href="./help/rf-groupterms/index.html#normal-subgroup">normal subgroup</a>
            ${MathML.sans(MathML.sub('H', g.subgroupIndex))}
            (<a href="./help/rf-groupterms/index.html#isomorphism-isomorphic">isomorphic</a> to
            ${makeGroupRef(g.subgroupIsomorphicTo)}) gives
            ${makeGroupRef(g.quotientIsomorphicTo)}.</li>
      </template>
      <template id="decomposition_termination">
         <li>The group ${makeGroupRef(g)} is
            <a href="./help/rf-groupterms/index.html#abelian-group">abelian</a>.</li>
      </template>
      <template id="unsolvable">
         ${MathML.sans(group.name)} is not a <a href="./help/rf-groupterms/index.html#solvable-group-solvable-decomposition">solvable</a>
         group.
      </template>
      <template id ="simple">
         In fact, it does not even have a
         <a href="./help/rf-groupterms/index.html#normal-subgroup">normal subgroup</a>
         that can be used to form an <a href="./help/rf-groupterms/index.html#abelian-group">abelian</a>
         <a href="./help/rf-groupterms/index.html#quotient-group">quotient</a> group.
      </template>
      <template id="failure">
         <p>Group Explorer is currently unable to determine whether ${MathML.sans(group.name)} is a
            <a href="./help/rf-groupterms/index.html#solvable-group-solvable-decomposition">solvable</a> group because it does
            not have access to all the groups it needs. For example, there is a
            <a href="./help/rf-groupterms/index.html#normal-subgroup">normal subgroup</a>
            of order ${unknown_subgroup.order} that yields an
            <a href="./help/rf-groupterms/index.html#abelian-group">abelian</a>
            <a href="./help/rf-groupterms/index.html#quotient-group">quotient</a> group, but that is not
            <a href="./help/rf-groupterms/index.html#isomorphism-isomorphic">isomorphic</a> to any group in
            the library currently loaded.</p>
         <p>You will need to more groups loaded (see <a href="">options window</a> for starters)
            to make this computation possible.</p>
      </template>
      <div class="gapcode" data-built-in-code-type="is solvable"/>
   </body>
</html>
